Organizing committee: Seth Stein, Northwestern, chair (earth sciences) David A. Yuen, University of Minnesota (earth sciences) Maarten V. De Hoop, Purdue University (mathematics and earth sciences) Ridgway Scott, University of Chicago (mathematics) Jared Wunsch, Northwestern (mathematics) Michael Stein, University of Chicago (statistics) Peter Constantin, University of Chicago (mathematics) Raymond Pierrehumbert, University of Chicago (earth sciences) John Schotland, University of Michigan (mathematics and physics ) Mary Silber, Northwestern (applied math) Logistics: Allison Witt-Janssen, Shelley Levine, Tim Johnson, Reid Wellensiek (NU) Projection and video: Mike Knox,Jack Zhou,Chris Gonzalez, Dave Sanchez, Chris Spencer (Minnesota ) NSF support: Junping Wang (DMS); Robin Reichlin (EAR)

MOTIVATION Over the past two decades the geosciences have acquired a wealth of high quality data from new and greatly improved observing systems. Because this volume of data poses a major challenge for traditional analysis methods, only a fraction of its potential has been exploited. Similarly, although numerical simulations of earth processes are being common, much remains to be learned about how well these simulations reflect the real world or the model they simulate. Hence neither the data nor the modeling are being used to their full potential, leaving crucial questions unresolved. This situation arises in a wide range of areas including natural hazards, earthquake and volcano dynamics, earth structure & geodynamics, climate & weather, and planetary science. Making progress in part calls for the application of mathematical and statistical methods not currently used, which requires a deeper and long-term dialogue and interaction between the mathematical, statistical, and geoscience communities. This workshop, part of such ongoing efforts, seeks to help earth scientists, mathematicians, and statisticians identify and explore jointly crucial unsolved problems amenable to mathematical approaches not currently used. This seems feasible if these groups develop a long-term relationship giving each reasonable sophistication with the others’ language, problems, and techniques. To set the stage, the workshop will illustrate some areas in which collaborative efforts are likely to yield significant advances.

SOME POSSIBLE THEMES Understanding earth systems: development and validity of theoretical models, mathematical foundations (analysis, topology, geometry,..) Computation of processes in earth systems -- digital laboratory: accuracy, stability, very large systems, solution procedures (numerical analysis, numerical linear algebra, computational geometry, visualization,..) Characterization, uncertainty quantification, data requirements: common data model, fusion, exploiting nonlinear physical phenomena, new sensors? (inverse problems,..) Predicting earth system evolution: hazards, mechanisms, interface with (geo)biology, human interface (dynamical systems, high-dimensional problems, learning theory?,..) Multi-scale analysis, stochastic analysis: processes on all scales, catastrophes, extreme events,.., comparative analysis across systems

PROGRAMMATIC APPROACHES To date, now ending: NSF Collaboration in Mathematical Geosciences (CMG) Future possibilities: NSF Mathematical Sciences Institute NSF Science, Engineering and Education for Sustainability (SEES) research network to “engage and explore fundamental theoretical issues and empirical questions in sustainability science, engineering, and education” Research Networks in the Mathematical Sciences (RNMS) Private sector and/or foundations Other?

WORKSHOP PLAN Monday: student oriented lectures Tuesday - Thursday: keynote presentations to catalyze discussions Thursday - informal presentations Tuesday-Thursday following presentations: group discussions of needs and possible future programs Outcome: Start white paper on needs & programs

ACTIVITIES AND LOGISTICS Continental breakfast & lunches at meeting room Dinner at nearby restaurants (map in booklet) Seismic imaging experiment Wednesday after lectures

Our meeting site illustrates Earth’s warming climate

Great Lakes Atlas

Sella et al., 2007 GPS shows motion today due to ancient ice sheet Canada rises & US sinks Rate & pattern reflect ice load history & mantle viscosity

SOME POSSIBLE THEMES Characterizing the earth system from observations: What data are needed? What analysis methods need to be improved? Understanding earth system dynamics: How well do the numerical implementations of these models perform? (verification) How well do models simulate the physical system? (validation) Predicting earth system evolution: How well can we predict processes and hazards? How confident are we about the predictions? These are challenging intellectual questions with major societal significance

GPS: GLOBAL POSITIONING SYSTEM 24 Satellites 5-8 overhead most of the world Transmit radio signals Receivers on ground record signals and find their position from the time the signals arrive Positions used in many applications For tectonics, find motions from changes in position over time Stein & Wysession, 2003